We read newspapers and watch TV every day. There are many issues and many controversies. Since media are free, we can hear arguments from every possible side. How do we decide what is wrong or right? The first condition to accept a message is to understand it; messages that are too sophisticated are ignored. So it seems reasonable to assume that our understanding depends on our ability and our current knowledge. Here we show that the consequences of this statement are surprising and funny.

Humans are fundamentally social. They have progressively dominated their environment by the strength and creativity provided by and within their grouping. It is well recognised that human groups are highly structured, and the anthropological literature has loosely classified them according to their size and function, such as support cliques, sympathy groups, bands, cognitive groups, tribes, linguistic groups and so on. Recently, combining data on human grouping patterns in a comprehensive and systematic study, Zhou et al. identified a quantitative discrete hierarchy of group sizes with a preferred scaling ratio close to 3 , which was later confirmed for hunter-gatherer groups and for other mammalian societies. Using high precision large scale Internet-based social network data, we extend these early findings on a very large data set.

We study how firms select partners using a large database of publicly announced R&D alliances over a period of 25 years. We identify, for the first time, two distinct behavioral strategies of firms in forming these alliances. By reconstructing and analysing the temporal R&D network of 14,000 international firms and 21.000 publicly announced alliances, we find a «universal» behavior in firms changing between these strategies. In the first strategy, newcomers and nodes of low centrality initially establish links to nodes of similar or higher centrality.

We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k=−M to totally in favor k=M . Same-orientation agents persuade each other with probability p , becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q .

The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that–for the SIS model–differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node’s degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated).

The notion of a «rich-club» describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. Interestingly, the definition of a rich-club naturally emphasizes high degree nodes and divides a network into two subgroups. Our approach theoretically couples the underlying principle of a rich-club with the escape time of a random walker, and a rich-core is defined by examining changes in the associated persistence probability. The method is fast and scalable to large networks. In particular, we successfully show that the evolution of the core in \emph{C. elegans} and World Trade networks correspond to key development stages and responses to historical events respectively.

The friendship paradox states that your friends have on average more friends than you have. Does the paradox «hold'» for other individual characteristics like income or happiness? To address this question, we generalize the friendship paradox for arbitrary node characteristics in complex networks.

In this paper, we investigate the problem of how beliefs diffuse among members of social networks. We propose an information flow model (IFM) of belief that captures how interactions among members affect the diffusion and eventual convergence of a belief. The IFM model includes a generalized Markov Graph (GMG) model as a social network model, which reveals that the diffusion of beliefs depends heavily on two characteristics of the social network characteristics, namely degree centralities and clustering coefficients. We apply the IFM to both converged belief estimation and belief control strategy optimization. The model is compared with an IFM including the Barabasi-Albert model, and is evaluated via experiments with published real social network data.

We present a new type of spin market model, populated by hierarchical agents, represented as configurations of sites and arcs in an evolving network. We describe two analytic techniques for investigating the asymptotic behavior of this model: one based on the spectral theory of Markov chains and another exploiting contingent submartingales to construct a deterministic cellular automaton that approximates the stochastic dynamics. Our study of this system documents a phase transition between a sub-critical and a super-critical regime based on the values of a coupling constant that modulates the tradeoff between local majority and global minority forces. In conclusion, we offer a speculative socioeconomic interpretation of the resulting distributional properties of the system.

We empirically analyze five online communities: Friendster, Livejournal, Facebook, Orkut, Myspace, to identify causes for the decline of social networks. We define social resilience as the ability of a community to withstand changes. We do not argue about the cause of such changes, but concentrate on their impact. Changes may cause users to leave, which may trigger further leaves of others who lost connection to their friends. This may lead to cascades of users leaving. A social network is said to be resilient if the size of such cascades can be limited. To quantify resilience, we use the k-core analysis, to identify subsets of the network in which all users have at least k friends. These connections generate benefits (b) for each user, which have to outweigh the costs (c) of being a member of the network. If this difference is not positive, users leave. After all cascades, the remaining network is the k-core of the original network determined by the cost-to-benefit c/b ratio. By analysing the cumulative distribution of k-cores we are able to calculate the number of users remaining in each community.